If 1800 m°/d of wastewater from an industry has a BODs of 190
mg/L and k = 0.17/day (base 10)
a. How much oxygen is required to satisfy the demand for BODs of
this residue assuming that 1 kg of oxygen must be supplied by
kilogram of final BOD in the residue
b. What is the population equivalent of these wastes (besed in
BOD5)?

Answer:

The distance is 9 × 10¹⁰ m.

Step-by-step explanation:

Time (t) = 5 minute = 5 × 60s = 300 s

Now,

∴ Speed = Distance ÷ Time

∴ Distance = Speed × Time

d = 3 × 10⁸ × 300

d = 900 × 10⁸

d = 9 × 100 × 10⁸

d = 9 × 10¹⁰ m

Thus, The distance is 9 × 10¹⁰ m.

-TheUnknownScientist 72

Answer: there 28/29 days

Step-by-step explanation:

Answer: 28/29

Step-by-step explanation:

28 Days

29 Days for a leap year

Answer:

128 <33

Step-by-step explanation:

6 ÷ 3 + 32 • 4 - 2 = 128

▪︎▪︎▪︎▪︎▪︎▪︎

Answer:

525 in³

Step-by-step explanation:

Use the direct variation equation, y = kx.

Substitute y with v (volume) and substitute x with l (length) to represent this situation:

y = kx

v = kl

Plug in 35 as l and 15 as k, then solve for v (the volume):

v = kl

v = 15(35)

v = 525

So, the volume of the box is 525 in³

The value of the tangent TU for the circle with secant through U which intersect the circle at points V and W is equal to 12

Circle theorems are a set of rules that apply to circles and their constituent parts, such as chords, tangents, secants, and arcs. These rules describe the relationships between the different parts of a circle and can be used to solve problems involving circles.

For the tangent TU and the secant through U which intersect the circle at points V and W;

TU² = UV × VW {secant tangent segments}

(5x)² = 9 × 16

(5x)² = 144

5x = √144 {take square root of both sides}

5x = 12

x = 12/5

so;

TU = 5(12/5)

TU = 12

Therefore, the value of the tangent TU for the circle with secant through U which intersect the circle at points V and W is equal to 12

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In order to calculate the Mean Squared Error (MSE) for each region, you will need to have a dataset with values for each region.

Once you have this dataset, you can calculate the MSE using the following formula:

MSE = 1/n x ∑(yi - ŷi)²

where n is the number of data points in the region, yi is the actual value for the ith data point, and ŷi is the predicted value for the ith data point. Once you have calculated the MSE for each region, you can compare the values to determine if the variability around the fitted regression line is approximately the same for each region.

If the MSE values are similar for each region, then the variability around the fitted regression line is approximately the same. If the MSE values are different for each region, then the variability around the fitted regression line is not the same for each region.

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EXPLANATION

In order to turn -2x + 10y = 2 into slope-intercept form:

First, as we know, the generic slope-intercept form is:

y= mx + b

where m is the slope and b is the y-intercept

Going back to our equation:

-2x + 10y = 2

Adding +2x to both sides:

-2x + 2x + 10y = 2 + 2x

Adding similar terms:

10y = 2 + 2x

Dividing both sides by 10:

10y/10 = 2/10 + 2x/10

Simplifying:

y = 1/5 + x/5 --> Slope-intercept form

Answer:

-5z - 10

Step-by-step explanation:

Subtract 9z from 4z.

The sum of a positive number and a negative number is always positive.

So:

Let:

a = arbitrary number where a>0

b = another arbitrary number where b<0

According to the conjecture:

a + b > 0

However, this isn't true because:

For example:

a = 2 ; 2>0

b = -8 ; -8 < 0

2 + (-8) > 0

2 - 8 > 0

-6 > 0 ------> This is false, therefore the conjecture is false

To find the length of the graph of f(x)=ln(4sec(x)) for 0≤x≤π/3, we first need to compute the derivative of the function.

f(x) = ln(4sec(x))
f'(x) = (1/sec(x)) * (4sec(x)) * tan(x) = 4tan(x)
Next, we use the arc length formula:
L = ∫ [a,b] √[1 + (f'(x))^2] dx
Substituting in the values, we get:
L = ∫ [0,π/3] √[1 + (4tan(x))^2] dx
We can simplify this by using the identity 1 + tan^2(x) = sec^2(x):
L = ∫ [0,π/3] √[1 + (4tan(x))^2] dx
 = ∫ [0,π/3] √[1 + 16tan^2(x)] dx
 = ∫ [0,π/3] √[sec^2(x) + 16] dx
 = ∫ [0,π/3] √[(1 + 15cos^2(x))] dx
 = ∫ [0,π/3] √15cos^2(x) + 1 dx
Using the substitution u = cos(x), we get:
L = ∫ [0,1] √(15u^2 + 1) du
This can be solved using trigonometric substitution, but the details are beyond the scope of this answer. The final result is:
L = 4/3 * √(15) * sinh^(-1)(√15/4) - √15/2
Therefore, the length of the graph of f(x)=ln(4sec(x)) for 0≤x≤π/3 is approximately 3.195 units.

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Answer:

Step-by-step explanation:

Since one side of the square is 16 cm, the diameter of the circle is also 16 cm. Which means that the radius is 8. the area of a circle is pi times radius square. so it is pi times 8 squared, which is 64pi

The correct statements are:

The triangle and trapezoid area formulas have 1/2.

The parallelogram and rectangle formulas are both the same.

In the trapezoid formula, the bases are added.

A triangle is a polygon with three sides and three vertices. A triangle's angles add up to 180 degrees.

Area of a triangle = 1/2 x base x height

A trapezium is a quadrilateral that is convex. A trapezium is made up of at least two parallel sides. Area of a trapezium = 1/2  x (sum of the lengths of the parallel sides) x height

A rectangle is a quadrilateral in two dimensions with four right angles. Area of a rectangle = length x width

A parallelogram is a quadrilateral with two parallel sides. The opposite sides equal in length

Area of a parallelogram = base x height

Hence, the correct statements are options (A), (B), and (D).

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The question seems to be incomplete the correct question would be:

A neighborhood was given a vacant lot in the shape of a rectangle on which to build a park. The neighborhood is

considering how to split up the area. Which statements about the formulas for finding areas are true? Check all that

apply.

A. The triangle and trapezoid area formulas have 1/2.

B. The parallelogram and rectangle formulas are both the same.

C. In the parallelogram formula, the bases are added.

D. In the trapezoid formula, the bases are added.

E. In the triangle formula, the sides are added, then multiplied by 1/2​

The next three terms of the sequence will be 4,10,16.

What is a sequence?

A sequence is a list of numbers (or elements) that exhibits a particular pattern. For example, Olivia has been offered a job with a starting monthly salary of $1000 with an annual increment of $500. Can you calculate her monthly salary in the first three years? It will be $1000, $1500, and $2000. Observe that Olivia's salary over a number of years forms a sequence as they follow a pattern where the numbers are increasing by an amount of $500 every time.

Some of the most common examples of sequence are:

Arithmetic Sequences

A sequence in which every term is created by adding or subtracting a definite number from the preceding number is an arithmetic sequence.

Geometric Sequences

A sequence in which every term is obtained by multiplying or dividing a definite number with the preceding number is known as a geometric sequence.

Harmonic Sequences

A series of numbers is said to be in harmonic sequence if the reciprocals of all the elements of the sequence form an arithmetic sequence.

Fibonacci Numbers

Fibonacci numbers form an interesting sequence of numbers in which each element is obtained by adding two preceding elements and the sequence starts with 0 and 1. Sequence is defined as, F0 = 0 and F1 = 1 and Fₙ = Fn-1 + Fn-2

Now,

Given first term=-2

difference is =6

Therefore,

               The next three terms of arithmetic sequence will be -2+6,-2+6+6,-2+6+6+6  i.e. 4,10,16.

Hence,

          The next three terms of the sequence will be 4,10,16.

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The dimensions of the rectangle such that the rectangle have the greatest area is length  = 8 and width = 4   .

In the question ,

it is given that ,

a rectangle is inscribed with its base on the x axis , and its upper corner on the parabola y = 12 − x²  ,

let the coordinate of the upper right corner be P(x,y) ,

and A be the area of the rectangle .

the point P lies on the parabola , given y = 12 − x² ,

So,  P = P(x,12−x²)

Due to symmetry of the rectangle,  the width of rectangle is half the distance between P and the y axis ,

that means width = 2x   and length = y .

Area of the rectangle = width × Length

= 2x * y

= 2x (12 − x²)

= 24x - 2x³

To maximize the area we differentiate Area with respect to x ,

we get ,

dA/dx = 24 - 6x²

for critical point dA/dx = 0 ,

24 - 6x²  = 0

6x² = 24

x² = 4

x = ±2 ,

since length cannot be negative ,

So , x = 2 .

to check for maximum and minimum ,we differentiate Area with respect to x,

we get

d²A/dx² = -12x

substituting , x = 2 ,

we get -12 < 0, So , the area is maximum .

hence the width = 2*2 = 4

and length = 12 - 4 = 8

and the maximum area is 32 .

Therefore , The dimensions of the rectangle such that the rectangle have the greatest area is length  = 8 and width = 4   .

The given question is incomplete , the complete question is

A rectangle is inscribed with its base on the x axis and its upper corners on the parabola y = 12 − x² . What are the dimensions of such a rectangle with the greatest possible area ?

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Answer:

12x + 5y

8 hours = 101

Step-by-step explanation:

12/hr and 5/day

12x + 5y

8 hours = 12(8) + 5(1)

8 hours = 101

The total area of the regular pentagon prism is 485 square units

The given parameters are:

Base area = 50

Height = 11

Base = 7

Start by calculating the total area of the 5 sides using

Sides = n * Height * Base

Sides = 5 * 11 * 7

Sides = 385

The total surface area is

Total = 2 * Base area + Sides

This gives

Total = 2 * 50 + 385

Evaluate

Total = 485

Hence, the total area of the regular pentagon prism is 485 square units

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Answer:

x = 6 , y= -2

Step-by-step explanation:

=1 ( 2x + 3y =6)

2( x+y=4)

2x+3y =6 (1)

2x+2y = 8 (2)

by eq 1 and 2 using elimination method

y = -2

putting y in eq 2

2x + 2(-2)=8

2x -4 =8

2x =8+4

2x=12

x= 6

Answer:

x = 6 ,  y = -2

Step-by-step explanation:

2 x + 3 y = 6  (Equation 1)

x + y = 4        (Equation 2)

Solving by substitution :

(Equation 2) ⇒ y = 4 - x

Substitute y by 4 - x in (equation 1) :

2 x + 3 (4 - x) = 6

Then

2 x + 12 - 3x = 6

Then

12 - x = 6

Then

12 - 6 = x

Then

x = 6

We obtain :

y = 4 - x and x = 6

Then

y = 4 - 6

  = -2

Answer:

you use division then add then you get the answer

Step-by-step explanation:

x = 10 & y = 5 are the coordinates of the vertices of A'B'C'.

To find out what are the coordinates of the vertices of A'B'C' :

We are required to find reflected co-ordinates of triangles of the vertices A'B'C' followed by translation T(3,3).

Step 1

First we required to find translation T(3,3) of triangles vertices

A(2,7), B(6,7), C(4,5)

So translation T(3,3) of all 3 vertices

New Vertices are

Vertex A = 2+3 = 5

              = 7+6 = 10   \(A^{'}(5,10)\)

Vertex B = 6+3 = 9

              = 7+3 = 10   \(B^{'}(9,10)\)

Vertex C = 4+3 = 7

              = 5+3 = 8     \(C^{'}(7,8)\)

So, new vertices after translation T(3,3)

are \(A^{'}(5,10)\), \(B^{'}(9,10)\), \(C^{'}(7,8)\)

Step 2

Now we find reflection of these vertices about line passes through point P(10,8) & Q(0,-2)

= \(y-y_{1} = x-x_{1}\)

As we know reflection of a point \((x_{1}, y_{1})\) about a line ax+by+c > 0 is

\(\frac{x-x_{1} }{a} = \frac{y-y_{1} }{b} = -2\frac{(ax_{1}+by_{1}+c) }{a^{2}+ b^{2} }\)

where x+y  -> reflected point

1. Reflection of (5,10) about x-y-2 = 0

\(\frac{x-5}{1} = \frac{y-10}{-1} = \frac{-2(5-10-2)}{1^{2}+ 1^{2} }\)

\(\frac{x-5}{1} = \frac{y-10}{-1} = \frac{-2(-7)}{2}\)

\(\frac{x-5}{1} = \frac{y-10}{-1} = 7\)

x-5 = 7       y-10 = -7

x = 12        y = 3

\(A^{''}(12,3)\)

2. Reflection of (9,10) about x-y-2 = 0

\(\frac{x-9}{1} = \frac{y-10}{-1} = \frac{-2(1x9+(-1)10+(-2))}{1^{2}+ 1^{2} }\)

\(\frac{x-9}{1} = \frac{y-10}{-1} = \frac{6}{2}\)

x-9 = 3       y-10 = -3

x = 12        y = 7

\(B^{''}(12,7)\)

3. Reflection of (7,8) about x-y-2

\(\frac{x-7}{1} = \frac{y-8}{-1} = \frac{-2(7-8-2)}{1^{2}+ 1^{2} }\)

\(\frac{x-9}{1} = \frac{y-10}{-1} = -1(-3)\)

x-7 = 3 & y-8 = -3

x = 10 & y = 5

Hence the answer is x = 10 & y = 5 are the coordinates of the vertices of A'B'C' after a reflection across a line through point P with a y-intercept

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F(1000) can be expressed in terms of F(998) and F(997) as 2F(998) + F(997). This means that to calculate F(1000), we only need to know the values of F(998) and F(997).

(a) According to the recurrence relation for the Fibonacci sequence in Definition 3.1, we have:

F(0) = 0, F(1) = 1, and F(n) = F(n-1) + F(n-2) for n ≥ 2.

To answer Fibonacci's question and calculate F(12), we can use the recurrence relation as follows:

F(2) = F(1) + F(0) = 1 + 0 = 1

F(3) = F(2) + F(1) = 1 + 1 = 2

F(4) = F(3) + F(2) = 2 + 1 = 3

F(5) = F(4) + F(3) = 3 + 2 = 5

F(6) = F(5) + F(4) = 5 + 3 = 8

F(7) = F(6) + F(5) = 8 + 5 = 13

F(8) = F(7) + F(6) = 13 + 8 = 21

F(9) = F(8) + F(7) = 21 + 13 = 34

F(10) = F(9) + F(8) = 34 + 21 = 55

F(11) = F(10) + F(9) = 55 + 34 = 89

F(12) = F(11) + F(10) = 89 + 55 = 144

Therefore, F(12) = 144.

(b) To find F(1000) in terms of F(999) and F(998), we can use the recurrence relation as follows:

F(1000) = F(999) + F(998)

To express F(999) in terms of F(998) and F(997), we have:

F(999) = F(998) + F(997)

Substituting this into the previous equation, we get:

F(1000) = F(998) + F(997) + F(998)

Simplifying this expression, we obtain:

F(1000) = 2F(998) + F(997)

Therefore, F(1000) can be expressed in terms of F(999) and F(998) as 2F(998) + F(997).

(c) To write F(1000) in terms of F(998) and F(997), we can use the recurrence relation as follows:

F(1000) = F(999) + F(998)

Substituting F(999) with its expression in terms of F(998) and F(997), we get:

F(1000) = F(998) + F(997) + F(998)

Simplifying this expression, we obtain:

F(1000) = 2F(998) + F(997)

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Answer:

Step-by-step explanation:

.

For positive acute angles A and B, it is known that sin A= 4/5 and tan B= 45/28 . Find the value of IIT A+B in simplest form. Question. user avatar image ...

the solution of sin(A + B) in simplest form is 27/35.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, We use the trigonometric identity as;

sin(A + B) = sin A cos B + cos A sin B

Hence, we need to find cos A and cos B.

Here, We know that;

⇒ sin A = 4/5,

By use the Pythagorean identity;

sin²A + cos² A = 1

sin² A + cos² A = 1

(4/5)² + cos² A = 1

16/25 + cos² A = 1

cos² A = 9/25

cos A = 3/5

And, we can use the identity;

tan B = sin B / cos B

to find sin B:

tan B = sin B / cos B

45/28 = sin B / √(1 - sin² B)

(45/28)² = sin² B / (1 - sin² B)

sin² B + (45/28)² sin² B = (45/28)²

sin² B (1 + (45/28)²) = (45/28)²

⇒ sin B = 3/7

Now that we have sin A, cos A, sin B, and cos B,

We can put them into the formula for sin(A + B):

sin(A + B) = sin A cos B + cos A sin B

sin(A + B) = (4/5)(45/28) + (3/5)(3/7)

sin(A + B) = 27/35

Therefore, the solution of sin(A + B) in simplest form is 27/35.

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The y-axis is the line of reflection that converts polygon VWXYZ to polygon V'W'X'Y'Z'.

A polygon is a two-dimensional geometric object that is created by connecting a series of points, known as vertices, with straight lines.

The y-axis is the line of reflection.

By comparing the locations of the vertices in the two polygons, we can see this.

While all of the vertices of polygon VWXYZ are situated in the upper half of the coordinate plane, all of those of polygon V'W'X'Y'Z' are situated in the bottom.

Each vertex in the polygon VWXYZ will be reflected to a corresponding point on the other side of the y-axis while retaining the same distance from the y-axis when we reflect the polygon across the y-axis.

As a result, a new polygon that is similar to the original polygon but has the opposite orientation will be created.

Similar to this, each vertex of the polygon V'W'X'Y'Z' will be mirrored across the y-axis to a corresponding point on the opposite side of the y-axis while retaining the same distance from the y-axis.

As a result, a new polygon that is similar to the original polygon but has the opposite orientation will be created.

Consequently, the y-axis is the line of reflection that converts polygon VWXYZ to polygon V'W'X'Y'Z'.

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Answer:

The y-axis is the line of reflection that converts polygon VWXYZ to polygon V'W'X'Y'Z'.

Step-by-step explanation:

The player is expected to lose money over time by playing this game. Therefore, paying 10 cents to play is not a fair price.

Based on the information given, the game pays out different amounts for getting different combinations of heads when tossing 3 fair coins. The payout is 21 cents for 3 heads, 10 cents for 2 heads, and 88 cents for 1 head. The question is whether paying 10 cents to play this game is a fair price.

To determine if the price is fair, we need to calculate the expected winnings. The probability of getting 3 heads is 1/8, the probability of getting 2 heads is 3/8, and the probability of getting 1 head is 3/8. The probability of getting 0 heads (or 3 tails) is also 1/8.

To calculate the expected winnings, we multiply the probability of each outcome by the amount that is paid out for that outcome, and then add up the results.

Expected winnings = (1/8 x 21) + (3/8 x 10) + (3/8 x 88) + (1/8 x 0)
Expected winnings = 2.625 + 3.75 + 33 + 0
Expected winnings = 39.375 cents

Since the expected winnings are higher than the cost to play (10 cents), the game is not fair.

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Answer:

y=4(5) =20

Step-by-step explanation:

The estimated current total cost for the installed and insulated tank is $12,065.73.

The first step is to calculate the surface area of the tank. The surface area of a cylinder is calculated as follows:

surface_area = 2 * pi * r * h + 2 * pi * r^2

where:

r is the radius of the cylinder

h is the height of the cylinder

In this case, the radius of the cylinder is 1 meter (half of the diameter) and the height of the cylinder is 1 meter. So the surface area of the tank is:

surface_area = 2 * pi * 1 * 1 + 2 * pi * 1^2 = 6.283185307179586

The insulation will add a thickness of 0.05 meters to the surface area of the tank, so the total surface area of the insulated tank is:

surface_area = 6.283185307179586 + 2 * pi * 1 * 0.05 = 6.806032934459293

The cost of the insulation is $40 per square meter and the cost of labor is $95 per square meter, so the total cost of the insulation and labor is:

cost = 6.806032934459293 * (40 + 95) = $1,165.73

The original cost of the tank was $10,900, so the total cost of the insulated tank is:

cost = 10900 + 1165.73 = $12,065.73

Therefore, the estimated current total cost for the installed and insulated tank is $12,065.73.

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Option A. If the alternative hypothesis of the test had been lower-tailed instead of two-tailed, the conclusion of the test would be different.

Recall that a two-tailed test is used when the alternative hypothesis is that the population parameter is different from the null hypothesis value in any direction, while a lower-tailed test is used when the alternative hypothesis is that the population parameter is less than the null hypothesis value.

In the given scenario, if the alternative hypothesis of the test had been lower-tailed instead of two-tailed, we would have tested the following null and alternative hypotheses:

H0: Pharaoh's translation is not worse than the other software's translation.

Ha: Pharaoh's translation is better than the other software's translation.

In this case, we would have calculated the p-value for the lower tail of the sampling distribution, and compared it to the significance level alpha. If the p-value is less than alpha, we would reject the null hypothesis and conclude that Pharaoh's translation is better than the other software's translation. If the p-value is greater than alpha, we would fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that Pharaoh's translation is better than the other software's translation.

Therefore, the correct answer to the question is option A: Unlike the two-tailed test, we would conclude that there is a difference between Pharaoh's translation and the translation of the other software.

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The linear function y = 25x - 79 is plotted on a graph with x - intercept at 3.16

A graph of a linear function is a line that goes through the origin (0, 0). The line can be described by the equation y = mx + b, where m is the slope of the line and b is the y-intercept. The slope of the line can be positive, negative, zero, or undefined.

In this problem, the linear function given y + 4 = 25(x - 3) can be written in slope - intercept form and then plotted in a graph using a graphical calculator.

y + 4 = 25(x - 3), the linear function can written;

y + 4 = 25(x - 3) = y + 4 = 25x - 75 ;

This becomes y = 25x - 75 - 4;

Collecting like terms

y = 25x - 79

Plotting this on a graph;

The line passes through the x - axis at 3.16 which is the x - intercept

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